Pith Number

pith:YABSTXNC

pith:2026:YABSTXNCYTSTUK7W7XI7N3UIGF

not attested not anchored not stored refs resolved

Quandle presentations of surface knots in 4-manifolds and bridge numbers

Xiaozhou Zhou

Banded unlink diagrams give Wirtinger presentations for the fundamental quandle of any surface link in a 4-manifold.

arxiv:2605.14593 v1 · 2026-05-14 · math.GT

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\usepackage{pith}
\pithnumber{YABSTXNCYTSTUK7W7XI7N3UIGF}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

we give a Wirtinger type presentation of the fundamental quandle of surface links in arbitrary 4-manifolds

C2weakest assumption

that banded unlink diagrams extend directly to yield the quandle presentation in arbitrary 4-manifolds without additional topological restrictions

C3one line summary

A Wirtinger-type presentation for the fundamental quandle of surface links in arbitrary 4-manifolds is constructed, yielding infinite families of non-local knots with fixed bridge numbers in CP^2 # m CPbar^2.

References

18 extracted · 18 resolved · 0 Pith anchors

[1] Twisting spun knots , author=. Trans. Amer. Math. Soc. , volume=. 1965 , publisher= 1965

[2] 2-knots with the same knot group but different knot quandles , author=. J. Math. Soc. Japan , volume=. 2026 , publisher= 2026

[3] Twist-spun torus knots , author=. Proc. Amer. Math. Soc. , volume=

[4] Knots, groups, and , volume=

[5] Racks and links in codimension two , author=. J. Knot Theory Ramifications , volume=. 1992 , publisher= 1992

Receipt and verification

First computed	2026-05-17T23:39:05.224693Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c00329dda2c4e53a2bf6fdd1f6ee883161a5cdf32f15d46893ea5c23944ac277

Aliases

arxiv: 2605.14593 · arxiv_version: 2605.14593v1 · doi: 10.48550/arxiv.2605.14593 · pith_short_12: YABSTXNCYTST · pith_short_16: YABSTXNCYTSTUK7W · pith_short_8: YABSTXNC

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YABSTXNCYTSTUK7W7XI7N3UIGF \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: c00329dda2c4e53a2bf6fdd1f6ee883161a5cdf32f15d46893ea5c23944ac277

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "050d6503772d1ff09fc5bd2d55ffb536182a03532a67cac79bcc38fcccaf67f6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-05-14T09:02:26Z",
    "title_canon_sha256": "5b138ac727fb34d02315d4c56d5636bd852bfa8ebb088490daf163e1c50ca8c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14593",
    "kind": "arxiv",
    "version": 1
  }
}